Vortex Analysis of the Periodic Ginzburg-Landau Model

Aydi, Hassen; Sandier, Etienne

doi:10.1016/j.anihpc.2008.09.004

Aydi, Hassen ; Sandier, Etienne

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1223-1236.

MR Zbl

DOI : 10.1016/j.anihpc.2008.09.004

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     title = {Vortex {Analysis} of the {Periodic} {Ginzburg-Landau} {Model}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1223--1236},
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     zbl = {1171.35480},
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Aydi, Hassen; Sandier, Etienne. Vortex Analysis of the Periodic Ginzburg-Landau Model. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1223-1236. doi : 10.1016/j.anihpc.2008.09.004. http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.004/

Bibliographie
Cité par

[1] Abrikosov A., On the Magnetic Properties of Superconductors of the Second Type, Soviet Phys. JETP 5 (1957) 1174-1182.

[2] Aftalion A., Blanc X., Nier F., Lowest Landau Level Functional and Bargmann Spaces for Bose-Einstein Condensates, J. Funct. Anal. 241 (2) (2006) 661-702. | MR | Zbl

[3] Aftalion A., Serfaty S., Lowest Landau Level Approach in Superconductivity for the Abrikosov Lattice Close to $H_{c_{2}}$ , Selecta Math. (N.S.) 13 (2) (2007) 183-202. | MR | Zbl

[4] Alama S., Bronsard L., Sandier E., On the Shape of Interlayer Vortices in the Lawrence-Doniach Model, Trans. Amer. Math. Soc. 360 (2008) 1-34. | MR | Zbl

[5] Almog Y., On the Bifurcation and Stability of Periodic Solutions of the Ginzburg-Landau Equations in the Plane, SIAM J. Appl. Math. 61 (1) (2000) 149-171. | MR | Zbl

[6] Almog Y., Abrikosov Lattices in Finite Domains, Commun. Math. Phys. 262 (3) (2006) 677-702. | MR | Zbl

[7] H. Aydi, Doctoral Dissertation, Université Paris-XII, 2004.

[8] Bethuel F., Brezis H., Hélein F., Ginzburg-Landau Vortices, Progress in Nonlinear Partial Differential Equations and Their Applications, vol. 13, Birkhäuser Boston, Boston, 1994. | MR | Zbl

[9] Bethuel F., Rivière T., Vortices for a Variational Problem Related to Superconductivity, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (3) (1995) 243-303. | Numdam | MR | Zbl

[10] Brandt E. H., The Flux-Line Lattice in Superconductors, Rep. Prog. Phys. 58 (1995) 1465-1594.

[11] Comte M., Mironescu P., The Behavior of a Ginzburg-Landau Minimizer Near Its Zeroes, Calc. Var. Partial Differential Equations 4 (4) (1996) 323-340. | MR | Zbl

[12] Doria M. M., Gubernatis J. E., Rainer D., Solving the Ginzburg-Landau Equations by Simulated Annealing, Phys. Rev. B 41 (1990) 6335-6340.

[13] Du Q., Gunzburger M. D., Peterson J. S., Modeling and Analysis of a Periodic Ginzburg-Landau Model for Type-II Superconductors, SIAM J. Appl. Math. 53 (3) (1993) 689-717. | MR | Zbl

[14] Dutour M., Bifurcation Vers L'état D'Abrikosov Et Diagramme De Phase, Thèse Orsay. Available online at:, http://xxx.lanl.gov/abs/math-ph/9912011.

[15] Jerrard R. L., Lower Bounds for Generalized Ginzburg-Landau Functionals, SIAM J. Math. Anal. 30 (4) (1999) 721-746. | MR | Zbl

[16] Jerrard R. L., Soner H. M., The Jacobian and the Ginzburg-Landau Energy, Calc. Var. Partial Differential Equations 14 (2) (2002) 151-191. | MR | Zbl

[17] Kleiner W. H., Roth L. M., Autler S. H., Bulk Solution of Ginzburg-Landau Equations for Type II Superconductors: Upper Critical Field Region, Phys. Rev. 133 (1964) A1226-A1227. | Zbl

[18] Lasher G., Series Solution of the Ginzburg-Landau Equations for the Abrikosov Mixed State, Phys. Rev. 2 140 (1965) A523-A528. | MR

[19] Mironescu P., Les Minimiseurs Locaux Pour L'équation De Ginzburg-Landau Sont À Symétrie Radiale, C. R. Acad. Sci. Paris, Ser. I 323 (6) (1996) 593-598. | MR | Zbl

[20] Odeh F., Existence and Bifurcation Theorems for the Ginzburg-Landau Equations, J. Math. Phys. 8 (1967) 2351-2356.

[21] Sandier E., Serfaty S., On the Energy of Type-II Superconductors in the Mixed Phase, Rev. Math. Phys. 12 (9) (2000) 1219-1257. | MR | Zbl

[22] Sandier E., Serfaty S., Vortices in the Magnetic Ginzburg-Landau Model, Progress in Nonlinear Differential Equations and Their Applications, vol. 70, Birkhäuser Boston Inc., Boston, MA, 2007. | MR | Zbl

[23] E. Sandier, S. Serfaty, From the Ginzburg-Landau model to vortex lattice problems, in preparation.

[24] Serfaty S., Local Minimizers for the Ginzburg-Landau Energy Near Critical Magnetic Field, Part I, Comm. Contemp. Math. 1 (2) (1999) 213-254, part II, 295-333. | MR | Zbl

[25] Tinkham M., Introduction to Superconductivity, second ed., McGraw-Hill, New York, 1996.

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